Using linked employer-employee data from Brazil, we document a large gender pay gap due to women working at lower-paying employers. To interpret this fact, we develop an equilibrium search model with endogenous firm pay, amenities, and hiring. We provide a constructive proof of identification of all model parameters. The estimated model suggests that amenities are important for both men and women and that compensating differentials explain half of the gender pay gap. Equal-treatment policies partly close gender gaps but are not output- or welfare-improving.